You have a dial that goes from 1 to 9 and the dial steps by one each time …from 1 to two is one step from two to 3 is one step… without actually setting there and counting all the times it steps and without using divesion or multiplication but only addition if you start at one and take 123459999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
9999999999999999999999999999999999999999999999999999999999999999999992 steps what number will you land on?[/b]
I’ve seen a similar problem to this before, but as hinted in Carleas’s question, you missed an essential detail (one that was given in the similar problem I saw):
The messenger said “the monks may have the disease as well,” but in order for the problem to work, what he should have said is “At least one of the monks does, in fact, have the disease.” Otherwise none of the monks has to die.
But, assuming he did say that, I think the answer is around 30 (assuming that the period of time between meals is over 2 hours).
[edit]
come to think of it, maybe he doesn’t need to say that…I’m not sure.
In any case, my answer remains the same.
[edit2]
I’m still not sure, but I’m pretty confident he does need to say something to that effect…
This requires a conversion of this decimal number to nonal, and observing only the last digit (and adding it to the starting number in nonal).
But there is a simpler way to solve this puzzle as explained here (that achieves the same result):
[tab]One can simply rely on a property of decimal numbers and their divisibility by 9.
To illustrate this property: 9 steps would result in no change from the start number, and the same with 9 more steps (18 steps) etc. such that any number of steps divisible by 9 results in no change from the start number. Adding together the digits in decimal numbers divisible by 9 (e.g. 18, 27, 90, 99, 108, 900, 999, 99999999 etc.) always gives another number that is divisible by 9. Continually applying the same addition to the result, in case it is not a single digit result, will always eventually result in 0 if the number is divisible by 9.
If the number is not divisible by 9, the eventual result will be the remainder - or in the case of this puzzle, the offset from the starting point. This property allows us to eliminate the need for division as in the rules for solving this puzzle.
Applying this property to a number with any 9s in it makes any 9s redundant (since adding together any number of 9s with any number will not change the remainder when dividing the number by 9). So we can eliminate all the 9s in the huge beginning number, such that we are essentially dividing 123452 by 9 - or adding 1+2+3+4+5+2 to make 17 and then adding 1+7 to make 8.
Therefore taking the specified huge number of steps around a dial that goes from 1-9 will eventually offset the starting number by 8 steps.
Starting from 1, as the puzzle asks, and advancing 8 steps (to 2,3,4,5,6,7,8,9) will land us on 9.[/tab]
So I’m sorry, FJ but you’re wrong! (Due to a condition you forgot, mentioned in the last line of my above tabbed explanation.)
[tab]You’d have been right if the starting number was 9 (plus 8 sets the nonal dial to number 8 ). But it’s 1 (plus 8 sets the dial to number 9).[/tab]
I’ve finally got this one. Took me over 40 days… sheesh. (Albeit not thinking about it for much of that time by any means! I think I’ve only sat down and thought about it seriously about 3 or 4 times, but especially counting today this still amounts to a fair while. The one night of planning that the prisoners get probably wouldn’t have been enough for me.)
[tab]The prisoners must nominate a single “manager” to keep count of the number of times the lightbulb is switched OFF.
It is agreed that this “manager” will be the only prisoner who will ever switch ON the lightbulb. He will never switch it off.
Accordingly, the other 99 prisoners will never switch on the lightbulb, and they will only ever switch it OFF once each.
These are the rules, and things will unfold thus:
Non-manager prisoners can be chosen to visit the central living room any number of times before the manager’s first visit, but the lightbulb must remain OFF.
The first time the manager visits the room, the lightbulb will therefore still be in its initial OFF state. He switches ON the lightbulb.
If the manager is chosen two or more days in a row, he will find the lightbulb still ON. He will leave it on.
If a non-manager is chosen after the manager, he will find the lightbulb on and he will turn it OFF. He will never again turn the lightbulb either on or off.
If a non-manager prisoner follows a non-manager prisoner (whether himself or not), he will leave the lightbulb off.
The next time the manager enters the central living room after a non-manager, he will find the lightbulb OFF. He will count +1, and switch the lightbulb ON.
This pattern will continue until the manager has counted 99 non-manager prisoners. The next time he is picked after this point, he can be sure that the other 99 prisoners have been to the room by now, and now that he has (yet again), he can assert with 100% certainty that all 100 prisoners have been to the living room by now. Hello freedom and MENSA.
This works because the binary positions of the lightbulb account for 1: the manager and 0: everyone else. The manager can (and of course must be able to) count the zeroes (and himself, the one 1).[/tab]
Still flummoxed about this one, so I guess I’m not a philosopher. Maybe your clue about not being a philosopher if you can’t solve it is due to the whole lack of mirrors problem and identity issues associated with mirrors. But if that’s what you were getting at, I still don’t get it.
P.S. In my tabbed explanation for the nonal dial puzzle, I seem to have implied that dividing 9 by 9 gives you 0. Obviously a mistake, I meant 1.
Why Math Works ?
Because math tied with physics.
For example:
I say that there is circle-particle that can change /
transformed into sphere-particle and vice versa
and Euler’s equation cosx + isinx in = e^ix can explain
this transformation / fluctuation of quantum particle.
I try to understand more details.
I have circle- particle with two infinite numbers: (pi) and (e).
I say that this circle-particle that can change into sphere-particle
and vice versa. Then I need third number for these changes.
The third number, in my opinion, is infinite a=1/137
( the fine structure constant = the limited volume coefficient)
This coefficient (a=1/137) is the border between two
conditions of quantum particle. This coefficient (a=1/137) is
responsible for these changes. This coefficient (a=1/137) united
geometry with the physics ( e^2=ah*c)
=…
If physicists use string-particle (particle that has length but
hasn’t thickness -volume) to understand reality
(and have some basic problems to solve this task) then why don’t
use circle-particle for this aim.
It is a pity that I am not physicist or mathematician.
If I were mathematician or physicist I wouldn’t lost the chance
to test this hypothesis.
=…
Best wishes.
Israel Sadovnik Socratus
==…
[tab]No actually that is not necessary in the more difficult version of the problem, it does as you say not matter if you say at least 1 of the monks has the disease as it will become clear if you work through it. Clearly someone has it or the answer would not be how many people die, but why is everyone still alive? We know some monks are found dead in their beds, and we know some monks may have the disease. I know semantics, but it is important.[/tab]
I’ll let this run further before I say what the answer is.
That’s nice work but you or them or whatever need to work it through a little further. There is a way.
By the way when I say easier their both not easy but it is a matter of realtive ease. I solved both 1 on my own, the other with some help. No man is an island.
Well you are right about one of those, but let’s let it run. And the other one, excuse me saying you are not a philosopher, cause I am not, and that one I needed help on. Although I am told it is easier. It is a good exercise in logic, something I admit freely I was and nor still am one now. Maths I can do, the painstaking methodology of the solution is once you have an idea easy.
[tab]And by the way you don’t need a manager, but nonetheless your solution is correct. Might be interesting to think why if you can be bothered but frankly after spending all that time I’d probably not. I kinda had an epiphany when I did it about the switches, in fact I stumbled on the solution almost straight away, although the finer points needed some work, (one of those rare moments you just get inspired) and from then on it was a matter of 1,0 without needing necessarilly to know who had been in the room exactly. [/tab]
These sorts of things do not have just 1 answer. Which is why I like them.
Hmm. I went through quite a few alternative potential solutions before I found the one I did, and they all turned out to be flawed except the one I posted. Are you sure there is at least one other way? I cannot think of a way to do it aside from what I came up with because of that last line in my tabbed solution.
As for the monk one, I simply don’t know where to start:
[tab]If they are not allowed to communicate in any way then they will have to find out whether they have the large red spot on their head by themselves.
Yet if no mirrors are allowed, and they are not able to directly see their head by themselves, then they cannot find out whether they have the large red spot on their head by themselves either.
It doesn’t seem right to get past this by using any accidental or unconscious communication in your solution, because that is still disallowed.
Nor does it seem right to get past this by using any alternative reflective surface in your solution, since it would at least act like a mirror, and therefore be disallowed. Though perhaps that technicality could be forgiven, it still seems wrong.
And that doesn’t leave any other room for them to find out about a solely visual indication. And then there’s something special about 11 days? I just don’t get it.[/tab]
I just need a hint on where to start, really.
[tab]The monk thing drove me nuts at first until someone started me off on the right track. Ok so we know at least 1 monk has it, so start there, then work through what would happen if say 2 had it and so on. It’ll surprise you how it figures. Start with the simplest scenario, then use more complicated ones is the only hint I can give without giving it all away.
There is a non manager necessary I can show by which I mean just once does there have to be a person in the room who knows a condition, it’s just a different way of doing what you did, to which I say kudos, it’s basically about position of switches according to the first occurrence, rather than who is in the room, it’s entirely a solution that is no better or worse than that solution. An an optimal solution that then only relies on one time a situation is found, I found out about after I had solved it, that frankly introduced me to laws of probability I was completely unaware of, very interesting but I think if you want that solution, you should probably pm me. Suffice to say they should not be inducted into MENSA but hired by any think thank. Your solution is correct and the best given what you know, but is not optimal. [/tab]
The monk one starts with how you know you have it without mirrors or magic. It finishes with the only possible solution to those that do. I can say no more than that. But how would anyone know they have it given the original problem. Sight is a clue!
How does one perceive anything? Start with the most simplest of assumptions, someone must have it, who or how many have it and why? it’s a serial problem not an outright solution after one day as the problem states.
[tab]Ok another clue, some of the monks are found dead, it’s more than one. So you can rule out at least that the herald of doom had it, and none of the monks did at least on day 1 you have to know you have it to die, so 1 monk at least must have it from the start however we are neutral about the messenger. If one monk has it and everyone can see he has and that monk can see that, and people are dying day after day… You have to work it through each day from the “assumption” that at least 1 person has it who is a monk. Some monks die, it is not likely they will all die at once? It does only say some monks are found dead on the 11th day which only says that some people died on the final day, it does not say anything about the previous days, it might mean some had already died it is unlikely it means no one did… Tis a demon of language and assumption this one. It’s a pain in the ass because the only way some things can happen is if they are determined by previous days. So you have to be working all over then time period. [/tab]
And one more thing although I think most have given up: if people die on the last day… we can only assume that they were because they are… and? It’s a clever little bugger because when you have the solution you realise why the monks die, but it takes a little logic to determine when and where, and you need the final solution to see it clearly. It’s kinda like that puzzle where you have all the corner pieces when you start, but the edges and more importantly the filler piece details and how they are filled in are sometimes little more than intuition and guesswork until you can see the whole picture or at least part of it so you have to start filling it in like you might a jigsaw puzzle, jogging forward and backward across all parts of the puzzle.
Good thing about this is if you google it you will only find the simple solutions to the simpler problems. This one is by no means either simple nor does it have an absolute answer done in an absolute way, as are all the best puzzles, but there is one.
[tab]So we know because some monks die, that there is a monk, 1 at least, that has a dot on his head by deduction if not induction… If no monks had a dot no one would die and the last part of the problem would be a paradox, it’s just obviously logical, no one has a dot in the community it’s not contagious even if the original messenger had one, it is not certain anyone would die in fact it’s certain no one would.
The easier puzzle tells you this, but this is not the easier puzzle. So when someone dies… we know… what? Look closely at the language some of the monks may have it, not 1 of the monks may have it. Why would he not say some of the monks may have it if he knew only one by sight had it, since it is non contagious that would be illogical… why would he say some or 1 monks have it when he can see no one has it, so hence no one would know they had it, no one would die, and so on… And there’s more as well, and it goes for quite some time before you work your way to the one of the monks definitely has it, or more… It’s not easy, it’s a pain in the ass, it’s only virtue is it is logical.[/tab]
Damn no one will even try it. I must admit the first time I postulated this, no one would even try it, given to me I was much the same. Is there no answer then?
Clue: sometimes the best answer is the most inconvenient.
And clue 2 probably why I was called a bad philosopher was because of my assumptions, my mistakes and my lack of ability to reason. The person who invented this kinda got me thinking, that sometimes there is an answer, and the only way to find it is to try it out. And then… No more clues you can either get it or you can’t.
You can’t see any way of solving this well then why, how does one exhaust all logical possibilities by claiming you cannot see? I am certainly not clever enough to make a puzzle this good, but the man who did, was of course more clever than I or perhaps more wise.
I’m trying! I’m trying!
I get the start of process to find the solution but my mind is going around itself in circles…
I put myself in the position of one of the monks.
1st meal goes as follows -
If I know that 1 monk is sick but I don’t see a red dot, I must me the sick one and therefore die in 2 hours.
If I see a red dot, and everyone else(apart from sick monk) does too then I am not sick and the monk with the dot dies.
The same assumption goes for there being 1,2 or more monks if we know that there are that number sick…
But I don’t understand how we get to know from how many are sick originally to how many die after X days or X meals.
Now I have a head-ache and suspect that I may even have a red dot on my fore-head…
And I had rice for dinner…
If there was only 1 guy with a red dot on his head, he would see no red dots, and remember that the guy said, verbatim, “the monks may have the disease as well.”
He sees no red dots, and there’s no reason he necessarily has to have a red dot – the monks may have the disease, and they may not – so he doesn’t die at all.
Now, what if there are 2 guys? Guy 1 and Guy 2 – they each see one other person with a red dot, right? Guy 1 sees Guy 2, and vice versa. And they see that everyone else doesn’t have a red dot. So they know that there’s either 1 or 2 people with the disease. If there’s 1 person with the disease, it’s the other guy, but because of the logic above, he knows that the other guy doesn’t necessarily have to die, so when he sees that the other guy lives…well, nothing. Still each one thinks that he may have it, or he may not have it, so no one has to die.
And you can do similar logic for 3 guys, 4 guys, etc.
The only way this riddle really works is if you change the wording – it doesn’t work with ‘may’. The guy needs to say, ‘at least one of you DOES have the disease’ for it to work.
[/tab]